Let `A=[0-tan(alpha//2)tan(alpha//2)0]` and `I` be the identity matrix of order 2. Show that `I+A=(I-A)[cosalpha-sinalphasinalphacosalpha]` .

If A=[{:(0,"tan"(alpha)/(2)),("tan"(alpha)/(2),0):}] and I theidentity matrix of order 2, show that I+A=(I-A)[{:(cosalpha,-sinalpha),(sinalpha,cosalpha):}] .

If sin (3alpha) /cos(2alpha) < 0 If alpha lies in

if [ ( cos alpha, - sin alpha),(sin alpha, cos alpha)] and A +A^1 =I then alpha =……

Let A A=[{:(0,1),(0,0):}] , show that (aI+bA)^(n)=a^(n)I+na^(n-1)bA , where I is the identity matrix of order 2 and n in N .

prove that : tan(alpha)+2 tan(2alpha) +4(tan4alpha)+8cot(8alpha) = cot(alpha)

If Delta_(1) is the area of the triangle with vertices (0, 0), (a tan alpha, b cot alpha), (a sin alpha, b cos alpha), Delta_(2) is the area of the triangle with vertices (a sec^(2) alpha, b cos ec^(2) alpha), (a + a sin^(2)alpha, b + b cos^(2)alpha) and Delta_(3) is the area of the triangle with vertices (0,0), (a tan alpha, -b cot alpha), (a sin alpha, b cos alpha) . Show that there is no value of alpha for which Delta_(1), Delta_(2) and Delta_(3) are in GP.

If A is square matrix such that A^(2)=A , show that (I+A)^(3)=7A+I .

If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is (a) tan^2(alpha/2) (b) cot^2(alpha/2) (c) tan^2alpha (d) cotalpha/2

If tan""(alpha)/(2)andtan""(beta)/(2) are roots of the equation 8x^(2)-26x+15=0 then cos(alpha+beta) = …………